{"paper":{"title":"The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Horzela, G. Dattoli, K. A. Penson, K. G\\'orska, {\\L}. Bratek","submitted_at":"2016-11-19T21:29:24Z","abstract_excerpt":"We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern in the frequency domain $\\sim[1+(i\\omega\\tau_{0})^{\\alpha}]^{-\\beta}$ with $\\tau_{0}$ being some characteristic time. For $\\alpha = l/k< 1$ ($l$ and $k$ positive integers) and $\\beta > 0$ we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their \"dual\" domain. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06433","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}